Abstract
We adopt the concept of channel diagonalization to time-frequency signal expansions obtained by DFT filter banks. As a generalization of the frequency domain channel representation used by conventional orthogonal frequency-division multiplexing receivers, the time-frequency domain channel diagonalization can be applied to time-variant channels and aperiodic signals. An inherent error in the case of doubly dispersive channels can be limited by choosing adequate windows underlying the filter banks. We derive a formula for the mean-squared sample error in the case of wide-sense stationary uncorrelated scattering (WSSUS) channels, which serves as objective function in the window optimization. Furthermore, an enhanced scheme for the parameterization of tight Gabor frames enables us to constrain the window in order to define paraunitary filter banks. We show that the design of windows optimized for WSSUS channels with known statistical properties can be formulated as a convex optimization problem. The performance of the resulting windows is investigated under different channel conditions, for different oversampling factors, and compared against the performance of alternative windows. Finally, a generic matched filter receiver incorporating the proposed channel diagonalization is discussed which may be essential for future reconfigurable radio systems.
Highlights
Motivated by the heterogeneity of today’s world of wireless communications—which includes cellular mobile radio systems of the second and third generations and beyond, wireless local and personal area networks, broadband wireless access systems, digital audio and video broadcast, emerging peer-to-peer radio, and so forth—particular attention is given to reconfigurable radio architectures
We show that the design of windows optimized for wide-sense stationary uncorrelated scattering (WSSUS) channels with known statistical properties can be formulated as a convex optimization problem
Making use of a suitable parameterization of tight frames, we have shown that the optimization of paraunitary Discrete Fourier Transform (DFT) filter banks for given channel statistics and oversampling factors can be formulated as a convex optimization (CO) problem
Summary
Motivated by the heterogeneity of today’s world of wireless communications—which includes cellular mobile radio systems of the second and third generations and beyond, wireless local and personal area networks, broadband wireless access systems, digital audio and video broadcast, emerging peer-to-peer radio, and so forth—particular attention is given to reconfigurable radio architectures. The cyclic extensions in OFDM signals facilitate a frequency domain representation of the multipath channel in the form of parallel single-tap lines. On the basis of the frequency domain signal description resulting from the blockwise Discrete Fourier Transform (DFT), the signal mapping by multipath channels can be represented as diagonal matrices. The signal transform associated with discrete-time tight Gabor frames fulfills Parseval’s identity This property is crucial for flexible receivers as it lets the correlation between two time domain signals be computed based on the respective TF signal representations. A main concern of this paper is the design of tight Gabor frames facilitating TF domain channel diagonalization with minimal model error for given channel conditions. Optimized windows can be computed off-line for different channel conditions encountered by reconfigurable receivers, such as the generic matched filter-based inner receiver discussed in this paper. E[·] denotes the expected value, R(·) and I(·) represent the real and imaginary parts, respective√ly, of complex arguments, mod the modulo operation, j −1, and x max{n ∈ Z : n ≤ x}
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